2. he foliowing questions, abed, and 9 refer to the table below. Dl D2 16 D3 Sup
ID: 369402 • Letter: 2
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2. he foliowing questions, abed, and 9 refer to the table below. Dl D2 16 D3 Supply 100 40 D4 20 SI 30 50 20 S2 129 14 10 40 S3 100 164 60 45 15 Dem 30 and 50 65 a. Read off the optinal x values and compute the optinal value b. Note that route S2-D3 is not being used at optinality. Your boss says what will happen tay costs if I ship 1 unit along S2-D3 anyway? Read off the answer. c. Now compute the new solution in part, compute the se 1 value in b., and compare it with the optinal value of l in a. to verify your ansver in partb d. What is the nost you can ship along $2-03 at the rate established in part b above? e. Are there other optinal routes for this problea? (yes, no, inpossible to tell). If yes, what are those optinal routes and the anounts shippedExplanation / Answer
a) optimal x values are:
Objective value, z = 30*14+50*16+20*12+40*8+45*8+15*15 = 2365
b) In s2-d3, there are two numbers given as cost 10 and 9 . I consider 10 as the cost.
If we ship 1 unit along this route, then 1 unit less is shipped along route s2-d4, because of limited supply of s2; To make up for the demand of d4, 1 unit more is shipped along the route s3-d4 and to account for the supply of s3, 1 unit less is shipped along the route s3-d3
resulting impact on total cost = 10-8+15-8 = 9
The cost increases by 9
c) New solution in part b is following
New value of z = 30*14+50*16+20*12+1*10+39*8+44*8+16*15 = 2374
Increase in value of z = 2375-2365 = 9
This is the same as calculated in part b. Hence verified.
d) The maximum we can ship along this route is 40, because s2 can supply only 40
e) There are no other optimal routes for this problem.
Final Variable Name Value x11 s1 d1 30 x12 s1 d2 50 x13 s1 d3 20 x24 s2 d4 40 x33 s3 d3 45 x34 s3 d4 15Related Questions
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